Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America.
Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America.
PLoS One. 2022 Feb 9;17(2):e0263047. doi: 10.1371/journal.pone.0263047. eCollection 2022.
Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.
当并非所有感染者都被报告时，将易感-感染-恢复（SIR）模型拟合到发病率数据上是有问题的。本文假设存在一个潜在的 SIR 模型，其恢复时间具有一般但已知的分布，当新感染个体的固定比例未被观察到时，本文推导出了观察到的发病率数据的隐含微分积分方程。所得微分方程组的参数是可识别的。使用这些微分方程，我们为当前疾病发病率的条件分布开发了一个随机模型，给定报告病例的整个过去历史。我们使用贝叶斯马尔可夫链蒙特卡罗抽样对后验分布进行参数估计。我们使用我们的模型来估计从 2020 年 1 月到 2021 年 5 月，美国、巴西、墨西哥、阿根廷、智利、哥伦比亚、秘鲁和巴拿马这八个美洲国家当前 2019 年冠状病毒爆发的传播率和无症状个体比例。我们的分析表明，报告病例的比例在所有国家都有所不同。例如，美国的报告发病率比例从 0.3 到 0.6 不等，而巴西的报告发病率比例从 0.2 到 0.4 不等。
